Question

Prove $\sum \limits_{k=0}^{n} (k+1){n \choose k} = 2^{n-1} (n+2)$

score 137 · Answer 1 · 2026-04-16 02:38:13

137

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Prove $\sum \limits_{k=0}^{n} (k+1){n \choose k} = 2^{n-1} (n+2)$

Published on 16 Apr 2026 - 2:38

score 33 · Answer 2 · 2026-04-14 13:45:30

33

Views

Proving and disproving inequalities constructively

Published on 14 Apr 2026 - 13:45

score 677 · Answer 3 · 2026-03-26 21:35:00

677

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Evaluating $\sum_{k=0}^\infty\sin(kx)$ and $\sum_{k=0}^\infty\cos(kx)$

Published on 26 Mar 2026 - 21:35

score 82 · Answer 4 · 2026-04-15 09:18:35

82

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$\int_{0}^{1} x \ dx$ without fundamental theorem of calculus

Published on 15 Apr 2026 - 9:18

score 54 · Answer 5 · 2026-04-13 19:54:10

54

Views

double sum $\sum_{i=1}^N\sum_{j=1}^N \vert i+1-j\vert$

Published on 13 Apr 2026 - 19:54

score 67 · Answer 6 · 2026-04-14 03:55:11

67

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Prove that $n\mid (n-1)!H_{n-1}$, where $n$ is an odd integer such that $n>1$

Published on 14 Apr 2026 - 3:55

score 192 · Answer 7 · 2026-04-15 14:45:52

192

Views

Show that $\sum_{i=1}^{k/2} {{k}\choose i}2^i < 3^{k-1}$

Published on 15 Apr 2026 - 14:45

score 39 · Answer 8 · 2026-04-09 16:06:23

39

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Estimation of summation

Published on 09 Apr 2026 - 16:06

score 100 · Answer 9 · 2026-04-09 19:13:36

100

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Why summation of sine function doesn't give the expected result?

Published on 09 Apr 2026 - 19:13

score 38 · Answer 10 · 2026-04-15 13:15:20

38

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evaluating $\sum_{n=0}^\infty \log\big(1+\frac{1}{2^{3^n}}+\frac{1}{2^{2\times{3^n}}}\big)$

Published on 15 Apr 2026 - 13:15

score 40 · Answer 11 · 2026-04-09 07:55:51

40

Views

Does this sum simplify?

Published on 09 Apr 2026 - 7:55

score 270 · Answer 12 · 2026-04-17 00:41:26

270

Views

Show that $(fg)^{(n)}(x)=\displaystyle\sum_{k=0}^n {n\choose k} f^{(n-k)}(x)g^{k}(x)$

Published on 17 Apr 2026 - 0:41

score 166 · Answer 13 · 2026-04-16 18:54:40

166

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Evaluate $\sum_{n=1}^{\infty} \left( \frac{\pi}{6} - \int_{0}^{n} \frac{\sqrt{3} (2x+1)}{(x^2+x+3)^2+3} dx \right)$

Published on 16 Apr 2026 - 18:54

score 56 · Answer 14 · 2026-04-11 16:29:51

56

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comparing two equations and obtaining some results

Published on 11 Apr 2026 - 16:29

score 39 · Answer 15 · 2026-04-15 22:00:46

39

Views

An application of partial summation to estimate the sum $\sum_{\mathbf{x}} 1/ \sqrt{x_1^4 + x_1^2x_2^2 + x_2^4 }$

Published on 15 Apr 2026 - 22:00

List Question

Prove $\sum \limits_{k=0}^{n} (k+1){n \choose k} = 2^{n-1} (n+2)$

Proving and disproving inequalities constructively

Evaluating $\sum_{k=0}^\infty\sin(kx)$ and $\sum_{k=0}^\infty\cos(kx)$

$\int_{0}^{1} x \ dx$ without fundamental theorem of calculus

double sum $\sum_{i=1}^N\sum_{j=1}^N \vert i+1-j\vert$

Prove that $n\mid (n-1)!H_{n-1}$, where $n$ is an odd integer such that $n>1$

Show that $\sum_{i=1}^{k/2} {{k}\choose i}2^i < 3^{k-1}$

Estimation of summation

Why summation of sine function doesn't give the expected result?

evaluating $\sum_{n=0}^\infty \log\big(1+\frac{1}{2^{3^n}}+\frac{1}{2^{2\times{3^n}}}\big)$

Does this sum simplify?

Show that $(fg)^{(n)}(x)=\displaystyle\sum_{k=0}^n {n\choose k} f^{(n-k)}(x)g^{k}(x)$

Evaluate $\sum_{n=1}^{\infty} \left( \frac{\pi}{6} - \int_{0}^{n} \frac{\sqrt{3} (2x+1)}{(x^2+x+3)^2+3} dx \right)$

comparing two equations and obtaining some results

An application of partial summation to estimate the sum $\sum_{\mathbf{x}} 1/ \sqrt{x_1^4 + x_1^2x_2^2 + x_2^4 }$

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